%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : KLE052+1 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n006.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Fri Oct 3 07:52:19 PM UTC 2025 % Result : Theorem 6.35s 6.52s % Output : Proof 6.35s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : KLE052+1 : TPTP v9.2.0. Released v4.0.0. % 0.11/0.13 % Command : duper %s % 0.13/0.34 % Computer : n006.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Thu Oct 2 16:58:08 EDT 2025 % 0.13/0.34 % CPUTime : % 6.35/6.52 SZS status Theorem for theBenchmark.p % 6.35/6.52 SZS output start Proof for theBenchmark.p % 6.35/6.52 Clause #0 (by assumption #[]): Eq (∀ (A B : Iota), Eq (addition A B) (addition B A)) True % 6.35/6.52 Clause #6 (by assumption #[]): Eq (∀ (A : Iota), Eq (multiplication one A) A) True % 6.35/6.52 Clause #8 (by assumption #[]): Eq (∀ (A B C : Iota), Eq (multiplication (addition A B) C) (addition (multiplication A C) (multiplication B C))) True % 6.35/6.52 Clause #12 (by assumption #[]): Eq (∀ (X0 : Iota), Eq (addition X0 (multiplication (domain X0) X0)) (multiplication (domain X0) X0)) True % 6.35/6.52 Clause #14 (by assumption #[]): Eq (∀ (X0 : Iota), Eq (addition (domain X0) one) one) True % 6.35/6.52 Clause #17 (by assumption #[]): Eq (Not (∀ (X0 : Iota), Eq (multiplication (domain X0) X0) X0)) True % 6.35/6.52 Clause #19 (by clausification #[6]): ∀ (a : Iota), Eq (Eq (multiplication one a) a) True % 6.35/6.52 Clause #20 (by clausification #[19]): ∀ (a : Iota), Eq (multiplication one a) a % 6.35/6.52 Clause #27 (by clausification #[0]): ∀ (a : Iota), Eq (∀ (B : Iota), Eq (addition a B) (addition B a)) True % 6.35/6.52 Clause #28 (by clausification #[27]): ∀ (a a_1 : Iota), Eq (Eq (addition a a_1) (addition a_1 a)) True % 6.35/6.52 Clause #29 (by clausification #[28]): ∀ (a a_1 : Iota), Eq (addition a a_1) (addition a_1 a) % 6.35/6.52 Clause #94 (by clausification #[14]): ∀ (a : Iota), Eq (Eq (addition (domain a) one) one) True % 6.35/6.52 Clause #95 (by clausification #[94]): ∀ (a : Iota), Eq (addition (domain a) one) one % 6.35/6.52 Clause #101 (by clausification #[8]): ∀ (a : Iota), % 6.35/6.52 Eq (∀ (B C : Iota), Eq (multiplication (addition a B) C) (addition (multiplication a C) (multiplication B C))) True % 6.35/6.52 Clause #102 (by clausification #[101]): ∀ (a a_1 : Iota), % 6.35/6.52 Eq (∀ (C : Iota), Eq (multiplication (addition a a_1) C) (addition (multiplication a C) (multiplication a_1 C))) True % 6.35/6.52 Clause #103 (by clausification #[102]): ∀ (a a_1 a_2 : Iota), % 6.35/6.52 Eq (Eq (multiplication (addition a a_1) a_2) (addition (multiplication a a_2) (multiplication a_1 a_2))) True % 6.35/6.52 Clause #104 (by clausification #[103]): ∀ (a a_1 a_2 : Iota), % 6.35/6.52 Eq (multiplication (addition a a_1) a_2) (addition (multiplication a a_2) (multiplication a_1 a_2)) % 6.35/6.52 Clause #107 (by superposition #[104, 29]): ∀ (a a_1 a_2 : Iota), % 6.35/6.52 Eq (multiplication (addition a a_1) a_2) (addition (multiplication a_1 a_2) (multiplication a a_2)) % 6.35/6.52 Clause #152 (by clausification #[12]): ∀ (a : Iota), Eq (Eq (addition a (multiplication (domain a) a)) (multiplication (domain a) a)) True % 6.35/6.52 Clause #153 (by clausification #[152]): ∀ (a : Iota), Eq (addition a (multiplication (domain a) a)) (multiplication (domain a) a) % 6.35/6.52 Clause #210 (by clausification #[17]): Eq (∀ (X0 : Iota), Eq (multiplication (domain X0) X0) X0) False % 6.35/6.52 Clause #211 (by clausification #[210]): ∀ (a : Iota), Eq (Not (Eq (multiplication (domain (skS.0 0 a)) (skS.0 0 a)) (skS.0 0 a))) True % 6.35/6.52 Clause #212 (by clausification #[211]): ∀ (a : Iota), Eq (Eq (multiplication (domain (skS.0 0 a)) (skS.0 0 a)) (skS.0 0 a)) False % 6.35/6.52 Clause #213 (by clausification #[212]): ∀ (a : Iota), Ne (multiplication (domain (skS.0 0 a)) (skS.0 0 a)) (skS.0 0 a) % 6.35/6.52 Clause #1403 (by superposition #[107, 20]): ∀ (a a_1 : Iota), Eq (multiplication (addition a one) a_1) (addition a_1 (multiplication a a_1)) % 6.35/6.52 Clause #1410 (by superposition #[1403, 153]): ∀ (a : Iota), Eq (multiplication (addition (domain a) one) a) (multiplication (domain a) a) % 6.35/6.52 Clause #1559 (by forward demodulation #[1410, 95]): ∀ (a : Iota), Eq (multiplication one a) (multiplication (domain a) a) % 6.35/6.52 Clause #1560 (by forward demodulation #[1559, 20]): ∀ (a : Iota), Eq a (multiplication (domain a) a) % 6.35/6.52 Clause #1563 (by backward contextual literal cutting #[1560, 213]): False % 6.35/6.52 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------